套代数中根理想的w~*闭包

THE w~* CLOSURE OF THE RADICAL OF NEST ALGEBRAS

利用零化子的技巧,完全刻划了套代数中根RN的w*闭包,得到Rw*N=W(RN∩K(H))**,其中Rw*N为RN的w*闭包,W={T∈B(H):P(N-)⊥TP(N)=0,N∈N};并且作为零化子和Rw*N刻划的应用,给出了RN中类Erdos稠密性定理的一个新的证明和距离公式dist(A,Rw*N)=supN‖P(N-)⊥AP(N)‖.

In this paper,the technique of annihilators is applied to characterize the w* closure of the radical RNin nest algebras,resulting in Rw*N=W ( RN∩ K( H) ) * * , where Rw*N is the w* closure of RNand W={T∈ B( H) :P( N- )⊥ TP( N) =0 , N∈ N}.Furthermore,as an application of annihilators and the characterization of Rw*N,a new proof of Erdos density theorem in RNand a distance formula dist( A,Rw*N) =sup N |P( N- )⊥ AP( N ) | are given.